Mark Rylance had been due to read the speech from The Tempest that is the inspiration for the Olympics opening ceremony's title, The Isles of Wonder. Photograph: Martin Godwin for the Guardian

Mark Rylance has pulled out of the London 2012 Olympics opening ceremony following the death of his 28-year-old step-daughter, the film-maker Nataasha van Kampen.

The actor had been due to take a central role in the Games opening ceremony, reading the speech from The Tempest that is the inspiration for the show's title, The Isles of Wonder.

In a statement, Rylance said Nataasha – the daughter of his wife Claire van Kampen and her former husband Chris van Kampen – died suddenly last Sunday. Rylance and Van Kampen married in 1992 and have another daughter, Juliet Rylance, Nataasha's elder sister.

He said: "Our beloved daughter and sister Nataasha passed away of unsuspected natural causes early on Sunday morning. Because of our bereavement, I have decided to withdraw from my commitment to the opening ceremony of the Olympics."

The Rylance family also asked "that their privacy is respected at this sad and difficult time".

Rylance added that he and his wife, who is a composer, would continue work on Richard III and Twelfth Night. The productions mark his welcome return to Shakespeare's Globe, a theatre he ran as artistic director between 1995 and 2005.

Richard III opens on 14 July and Twelfth Night, in which Rylance reprises a memorable role as Olivia, starts on 22 September before transferring to the West End's Apollo theatre.

Nataasha van Kampen was starting out in a career as a film-maker and had worked on commercials and documentaries.

Rylance revealed last month that he had been in two minds about appearing in the Olympics opening ceremony at all because of the corporate sponsorship.

In April he was a signatory to a letter in the Guardian in which he stated: "BP has no place in arts sponsorship."

He told the Radio 4 Today programme last month that he sympathised with critics of some of the Olympic sponsors. He said there were "big questions about BP, big questions about McDonald's and the amount of sugar and obesity that is costing the NHS millions.

"I have thought since agreeing [that] maybe I shouldn't be doing this. And if people feel critical of us who have taken part, I think they've got a point. But on the other hand, I think all these athletes have trained … So the human endeavour aspect of it is so wonderful that I wouldn't want it to stop. And I wouldn't want always to be a nay-sayer or a chastiser."

Rylance is one of Britain's finest stage actors, winning deserved acclaim most recently for his extraordinary performance as "Rooster" Byron in the Royal Court-originated play Jerusalem, which garnered an Olivier and a Tony.

It is thought that Rylance will continue with a pop-up Shakespeare project at the end of August, part of the London 2012 festival.